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,a< 

 XXI. On the Phanwmcna presented by Li ght in its Passage 

 along the Axes of Biaxal Ctystals. By the Rev. Humphrey 

 Lloyd, A.M. M.R.I. A. Fellow of Trinity College, and Pro- 

 fessor of Natural and Experimental Philosophy in the Uni- 

 versity of Dublin* . 



F T is well known that when a ray of light is incident upon 

 -■■ certain crystals, such as Iceland spar and quartz, it is in 

 general divided into two pencils, one of which is refracted ac- 

 cording to the known law of the sines, while the direction of 

 the other is determined by a new and extraordinary law first 

 assigned by Huyghens. -. 0ft 



These laws were long supposed to apply to all doubly-re- 

 fracting substances ; and it was not until the subject was taken 

 up by Fresnel, that the problem of double refraction was 

 solved in all its generality. Setting out from the hypothesis, 

 that the elasticity of the vibrating medium within the crystal 

 is unequal in three rectangular directions, Fresnel has shown 

 that the surface of the wave is neither a sphere nor a spheroid, 

 as in the Huyghenian law, but a surface of the 4th order, con- 

 sisting of two sheets, whose points of contact with the tangent 

 planes determine the directions of the two rays. From this 

 construction it follows that neither of the rays, in general, 

 obeys the law of Snellius, or that of Huyghens, but that they 

 are both refracted according to a new and more complicated 

 law. Such crystals have two optic axes, and are said to be 

 biaxal. When the elasticity of the medium is equal in two 

 of the three directions, the equation of the surface of the wave 

 is resolvable into two quadratic factors, which give the equa- 

 tions of the sphere and spheroid of the Huyghenian theory. 

 The two optic axes in this case coincide in one ; and the law 

 of Huyghens is thus deduced from the general solution, and 

 proved to belong to the case of uniaxal crystals. Final ly* 

 when the elasticity is equal in all the three directions, the sur- 

 face of the wave becomes a sphere; and the refraction is single, 

 and takes place according to the ordinary law of the sines. 



There are two remarkable cases, however, in this elegant 

 and profound theory, which its author seems to have over- 

 looked, if not to have misapprehended. In a communication 

 made, some months since, to the Royal Irish Academy, Pro- 

 fessor Hamilton has supplied these omissions in the theory of 

 Fresnel, and has thus been led to results in the highest de- 

 gree novel and remarkable. :d( jy 



To understand these conclusions, it will be necessary to 



Communicated bv the Author. 



A lo 



